2(x+1)+6x(x-1)=3x(x-3)

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Solution for 2(x+1)+6x(x-1)=3x(x-3) equation: 


Simplifying
2(x + 1) + 6x(x + -1) = 3x(x + -3)

Reorder the terms:
2(1 + x) + 6x(x + -1) = 3x(x + -3)
(1 * 2 + x * 2) + 6x(x + -1) = 3x(x + -3)
(2 + 2x) + 6x(x + -1) = 3x(x + -3)

Reorder the terms:
2 + 2x + 6x(-1 + x) = 3x(x + -3)
2 + 2x + (-1 * 6x + x * 6x) = 3x(x + -3)
2 + 2x + (-6x + 6x2) = 3x(x + -3)

Combine like terms: 2x + -6x = -4x
2 + -4x + 6x2 = 3x(x + -3)

Reorder the terms:
2 + -4x + 6x2 = 3x(-3 + x)
2 + -4x + 6x2 = (-3 * 3x + x * 3x)
2 + -4x + 6x2 = (-9x + 3x2)

Solving
2 + -4x + 6x2 = -9x + 3x2

Solving for variable 'x'.

Reorder the terms:
2 + -4x + 9x + 6x2 + -3x2 = -9x + 3x2 + 9x + -3x2

Combine like terms: -4x + 9x = 5x
2 + 5x + 6x2 + -3x2 = -9x + 3x2 + 9x + -3x2

Combine like terms: 6x2 + -3x2 = 3x2
2 + 5x + 3x2 = -9x + 3x2 + 9x + -3x2

Reorder the terms:
2 + 5x + 3x2 = -9x + 9x + 3x2 + -3x2

Combine like terms: -9x + 9x = 0
2 + 5x + 3x2 = 0 + 3x2 + -3x2
2 + 5x + 3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
2 + 5x + 3x2 = 0

Factor a trinomial.
(1 + x)(2 + 3x) = 0


Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1

Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {-1, -0.6666666667}

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